Question: Simplify the following expression: $ r = \dfrac{-1}{10} - \dfrac{y + 6}{-8y} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-8y}{-8y}$ $ \dfrac{-1}{10} \times \dfrac{-8y}{-8y} = \dfrac{8y}{-80y} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{y + 6}{-8y} \times \dfrac{10}{10} = \dfrac{10y + 60}{-80y} $ Therefore $ r = \dfrac{8y}{-80y} - \dfrac{10y + 60}{-80y} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{8y - (10y + 60) }{-80y} $ Distribute the negative sign: $r = \dfrac{8y - 10y - 60}{-80y}$ $r = \dfrac{-2y - 60}{-80y}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{y + 30}{40y}$